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Information
| Code | MT415 |
| Name | Coding Theory |
| Term | 2023-2024 Academic Year |
| Semester | 7. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. GONCA AYIK |
| Course Instructor |
Prof. Dr. GONCA AYIK
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course is to explain mathematical foundations of the coding theory to students.
Course Content
In this course source coding, uniquely decodable codes, instantaneous codes, Kraft and McMillan inequalities, optimal codes, binary Huffman codes, extensions of sources, information and entropy, Shannon Fano coding, Sahnnon first theorem, information channels, binary symmetric channels, using an unreliable channel, error-correction codes, linear coding are described.
Course Precondition
NONE
Resources
Information and coding theory, G. A. Jones and J.M. Jones, Springer, 2000.
Notes
Information and coding theory, G. A. Jones and J.M. Jones, Springer, 2000.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Realises the technical definition and is able to explain the concept of coding. |
| LO02 | Recognises different types of codes. |
| LO03 | Recognises the concepts of information and coding. |
| LO04 | Realises the basic theorems in Coding Theory |
| LO05 | Realises the error correction concepts. |
| LO06 | Realises Kraft and McMillan inequalities. |
| LO07 | Realises extensions of sources. |
| LO08 | Realises linear coding. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | 5 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to express the basic theories of mathematics both correctly. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 4 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | 5 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 5 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 4 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | 5 |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | 4 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 4 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 4 |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | 4 |
| PLO19 | Bilgi - Kuramsal, Olgusal | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Source coding | Reading the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Uniquely decodable codes, instantaneous codes | Reading the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Kraft and McMillan inequalities | Reading the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Optimal codes | Reading the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım, Tartışma |
| 5 | Binary Huffman codes | Reading the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Extensions of sources | Reading the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Information and entropy | Reading the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Review | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Shannon-Fano coding | Reading the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Shannon s First Theorem | Reading the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Information channels | Reading the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Binary symmetric channels | Reading the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım, Tartışma |
| 13 | Using an unreliable channel | Reading the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım, Tartışma |
| 14 | Linear coding | Reading the relevant parts of the textbook | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Review | Review | Öğretim Yöntemleri: Tartışma |
| 16 | Term Exams | Review | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||